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1328 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 4, APRIL 2014
Nonparametric Signal Processing Validation inT-Wave Alternans Detection and Estimation
R. Goya-Esteban∗, O. Barquero-Perez, M. Blanco-Velasco, Senior Member, IEEE, A. J. Caamano-Fernandez,A. Garcıa-Alberola, and J. L. Rojo-Alvarez, Senior Member, IEEE
Abstract—Although a number of methods have been proposedfor T-Wave Alternans (TWA) detection and estimation, their per-formance strongly depends on their signal processing stages andon their free parameters tuning. The dependence of the systemquality with respect to the main signal processing stages in TWAalgorithms has not yet been studied. This study seeks to optimizethe final performance of the system by successive comparisons ofpairs of TWA analysis systems, with one single processing differ-ence between them. For this purpose, a set of decision statisticsare proposed to evaluate the performance, and a nonparametrichypothesis test (from Bootstrap resampling) is used to make sys-tematic decisions. Both the temporal method (TM) and the spec-tral method (SM) are analyzed in this study. The experiments werecarried out in two datasets: first, in semisynthetic signals withartificial alternant waves and added noise; second, in two publicHolter databases with different documented risk of sudden cardiacdeath. For semisynthetic signals (SNR = 15 dB), after the optimiza-tion procedure, a reduction of 34.0% (TM) and 5.2% (SM) of thepower of TWA amplitude estimation errors was achieved, and thepower of error probability was reduced by 74.7% (SM). For Holterdatabases, appropriate tuning of several processing blocks, led toa larger intergroup separation between the two populations forTWA amplitude estimation. Our proposal can be used as a system-atic procedure for signal processing block optimization in TWAalgorithmic implementations.
Index Terms—Bootstrap resampling, electrocardiogram (ECG),signal processing, T-wave alternans (TWA).
I. INTRODUCTION
T -WAVE alternans (TWA) is a beat-to-beat fluctuation inthe amplitude, waveform, or duration of the ST-segment or
T-wave. TWA has been shown to be related to cardiac instabilityand increased arrhythmogenicity [1], [2]. Clinical studies sug-
Manuscript received August 3, 2013; revised November 15, 2013 and Jan-uary 7, 2014; accepted January 29, 2014. Date of publication February 4, 2014;date of current version March 17, 2014. This work was supported by ResearchProject TEC2010-19263. The work of O. Barquero-Perez was supported byFPU grant AP-2009-1726 from Spanish Government. Asterisk indicates corre-sponding author.
∗R. Goya-Esteban is with the Department of Signal Theory and Communica-tions, University Rey Juan Carlos, Fuenlabrada-28943, Madrid, Spain (e-mail:[email protected]).
O. Barquero-Perez, A. J. Caamano-Fernandez, and J. L. Rojo-Alvarez are withthe Department of Signal Theory and Communications, University Rey JuanCarlos, Fuenlabrada-28943, Madrid, Spain (e-mail: [email protected];[email protected]; [email protected]).
M. Blanco-Velasco is with the Department of Signal Theory and Communica-tions, Universidad de Alcala, 28801 Alcala de Henares, Madrid, Spain (e-mail:[email protected]).
A. Garcıa-Alberola is with the Arrhythmia Unit, Hospital Virgen de la Arrix-aca of Murcia, Murcia 30120, Spain (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBME.2014.2304565
gest that there is a patent relationship between large amplitudemicroscopic TWA and the risk of sudden cardiac arrest [2], [3].Therefore, TWA represents a strong marker of cardiac electricalinstability with relevant potential for arrhythmic risk stratifica-tion in adults [4]–[8], and it is also under research in fetus [9]. Anumber of methods have been proposed for TWA analysis, someof the most widely used are the spectral method (SM) [1], [2],[10], the complex demodulation (CD) method [11], the correla-tion method (CM) [12], methods based on the Karhunen-LoeveTransform [13], [14], the modified moving average (MMA)method [15], the Laplacian likelihood ratio method (LLR) [16],and the latest multilead analysis schemes [17].
An excellent taxonomy of the different approaches to TWAanalysis can be found in [18], which represents a state of art forthe vast amount of TWA algorithms proposed in the literature.Moreover, several different processing techniques are used tocondition the signal before the TWA detection and estimationstage [10], [12], [18], [19].
The comparison and validation of existing algorithms aretroublesome due to the lack of definition of a TWA clinical goldstandard. Moreover, the performance of the methods heavilydepends on their signal processing stages and parameter tuning,which are usually not optimized, but rather ad hoc selected fromprevious studies or experience [18]. To our best knowledge, aconstructive procedure to optimize the signal processing in TWAanalysis systems has not been proposed.
Therefore, this study aims to propose a systematic method-ology for optimizing the global performance of TWA analysissystems. For this purpose, we start from a TWA analysis systemcomposed of a set of signal processing blocks, and then, theeffect of a change in one single block (either inclusion vs exclu-sion, or free parameters tuning) is statistically quantified at thesystem output. A complete set of decision statistics is proposedto evaluate the performance of the system, in terms of centraltendency and dispersion of both detection and estimation qual-ity. The successive comparison of these pairs of TWA systemimplementations is then provided by means of nonparametrichypothesis tests (based on Bootsrap resampling). As a result,the significance of either the improvement or worsening of theglobal performance of the system can be determined.
Two different TWA analysis methods are used to test the pro-posed system optimization methodology. First, a simple imple-mentation for TWA amplitude estimation in the time domain,which is referred to as the TM. Second, the widely used SMapplied to both detect and estimate TWA.
Experiments were conducted in two datasets. First, onsemisynthetic signals composed of real ECG segments with
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GOYA-ESTEBAN et al.: NONPARAMETRIC SIGNAL PROCESSING VALIDATION IN T-WAVE ALTERNANS DETECTION AND ESTIMATION 1329
Fig. 1. Block diagram for the generic signal processing stages on a TWA analysis system. The system is composed of several processing stages, some of themdivided into processing blocks with a certain role in terms of signal processing. Input and output signals are defined for each block in the scheme.
artificial alternant waves and added noise. In this case, the pres-ence and amplitude of alternans are known; hence, a clear bench-mark can be stated for TWA estimation and detection. Second,experiments were also conducted on two Holter databases withdifferent documented risk of sudden cardiac death (SCD). Giventhe lack of benchmark for these data, the intergroup separationbetween the two databases for TWA amplitude estimation isused as the system optimization criterion.
The remainder of the paper is organized as follows. Section IIsummarizes the two TWA analysis methods used in this study,and Section III presents with detail the proposed optimizationprocedure and its statistical basis. The experiments and resultsare presented in Sections IV and V, for semisynthetic and Holterdatabases, respectively. Finally, the discussion and conclusionsare given in Section VI.
II. TWA ESTIMATION AND DETECTION METHODS
Fig. 1 depicts a diagram of a complete TWA analysis systemthat operates over a sliding ECG window length (L) of 128beats with 32 beats overlapping (D). Accordingly, s[n] denotesan ECG signal window to be analyzed.
The ECG preprocessing stage consists of two filtering blocks.First, high-frequency (HF) noise elimination with a coarse low-pass filter (CLPF) with zero-phase distortion and 50 Hz cutofffrequency, yielding an output signal sCLPF[n], which can be ex-pressed in terms of the mathematical operator ΓCLPF modifyings[n],
sCLPF[n] = ΓCLPF{s[n]} (1)
Second, baseline cancellation (BLC) accomplished through anLPF that in combination with spline interpolation, generatesa trend signal to be subtracted from sCLPF[n]. In this block,several design options are available. Let θi
b denote the ith freeparameter to be tuned during the design of block b; then θ1
BLCaccounts for the LPF type, and θ2
BLC is the window length forthe time interval between consecutive spline nodes. The outputsignal can be expressed using a mathematical transformationwith two free parameters,
sBLC [n] = ΓBLC{sCLPF[n], θ1BLC , θ2
BLC}. (2)
In the R-peak detection stage, R-peaks are detected onsBLC [n] using three consecutive blocks. First, a band-pass filter(BPF) is applied to preserve the spectral content of QRS com-plexes. The output signal of this block can be expressed in termsof the operator ΓBPF that has two free parameters, the centerfrequency (θ1
BPF ) and the bandwidth (θ2BPF ),
sBPF[n] = ΓBPF{sBLC [n], θ1BPF , θ2
BPF}. (3)
Second, the time instants of QRS complexes are determined onsBPF[n] by using an adaptive threshold, where a signal sample isselected as QRS index whenever it is higher than a given absoluteamplitude after a specified refractory period. The result is theset of QRS time instants, ni
qrs for i = 1, . . . , Q, where Q is thenumber of QRS complexes. The output signal can be expressedas qrs[n] =
∑Qi=1 δ[n − ni
qrs ], where δ[n] is the Kronecker deltafunction. Finally, R-peaks are determined on sBLC [n] by findingthe maximum amplitude in a time interval around each ni
qrs ,which yields the binary valued signal r[n] =
∑Qi=1 δ[n − ni
r ],with ni
r containing the temporal positions of R-peaks.Nonvalid beats discarding stage: TWA has been found to be
related to heart rate (HR) [20]–[22], and accordingly, ECG beatswith HR outside the band 40–120 beats/min are discarded, aswell as those RR intervals differing more than 50% from theprevious or the next ones. For each discarded beat, the alter-nant phase is preserved by also discarding the next beat. Notethat this approach does not take into consideration any possiblechange of phase of TWA, which would affect the estimation.To obtain accurate estimates with changes of phase, methods toestimate the phase of TWA should be implemented, as in [23].In our implementation, an ECG segment s[n] is fully discardedwhenever any of the following conditions are hold: 1) more than10 beats have been discarded and 2) the standard deviation ofRR intervals is larger than 10% of mean RR. The output signalof this block is given by the set of valid temporal positions ni
v ,for i = 1, . . . , M , with M ≤ Q, i.e., v[n] =
∑Mi=1 δ[n − ni
v ].Repolarization interval (ST-T) segmentation and synchro-
nization stage: Repolarization intervals are segmented and con-ditioned by using four consecutive blocks. First, a fine LPF(FLPF) is used to reject noise out of the TWA band (0.3–15 Hz) [24], and the output signal is expressed in terms of theoperator ΓFLPF with cutoff frequency θ1
FLPF as free parameter,
1330 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 4, APRIL 2014
i.e.,
sFLPF[n] = ΓFLPF{sBLC [n], θ1FLPF}. (4)
A subsequent block delineates each repolarization interval,yielding the output M × N matrix T, where M is the num-ber of valid beats in s[n], and N is the number of samples ofeach segmented repolarization interval. The free parameter θ1
T
corresponds to the segmentation type,
T = ΓT {sFLPF[n], θ1T }. (5)
Two different options are analyzed for θ1T . In option A, a fixed
segmentation is used, taking a 400 ms window after a 50 msgap following each R-wave. In option B, an RR-adjusted timewindow based on [12] is used. Three different T-wave onsets aredefined, namely, 60, 100, and 150 ms after the R peak for RR< 0.6, 0.6–1.1, and >1.1 s, respectively. The window length isobtained as 0.4
√mean(RR).
Next, the effect of possible high amplitude remaining samplesfrom the R–S segment in matrix T can be alleviated using anedge smoothing window (Tukey window with a ratio of taper toconstant section of 0.35) in each row of T. The output matrixof this block can be expressed in terms of the mathematicaloperator ΓW as follows:
Tw = ΓW {T}. (6)
Most works use at this point some alignment strategy [18];hence, the output matrix of the synchronization block can beexpressed in terms of the operator ΓSYN modifying Tw , with afree parameter θ1
SYN corresponding to the alignment strategy,
M = ΓSYN{Tw , θ1SYN}. (7)
Two different options are tested for θ1SYN . In option A, a
T-wave template, obtained as the median of 128 consecutiveT-waves, is used to align each wave by maximizing the crosscorrelation, allowing a variation of ±30 ms from its initial po-sition [12]. In option B, a normalization approach aims to alignthe samples of each complex corresponding to the same cardiacactivation instant from consecutive heartbeats. For this purpose,each segmented T-wave is normalized with respect to time, us-ing an interpolation rate given by the length of the segmentdivided by the length of the RR interval.
TWA detection and estimation stage: Now, M can be seen asa successive pattern of row vectors, Ai and Bi , consisting of Aand B heartbeat patterns plus additive noise vi , as follows:
M =
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
A1
B1
...
AM/2
BM/2
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
=
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
A
B...
A
B
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
+
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
v1
v2
...
vM −1
vM
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
. (8)
Ms is obtained as the difference of each pair of rows of M,
Ms =
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
A1 − B1
B1 − A2
...
AM/2 − BM/2
BM/2 − AM/2+1
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
=
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
−ε
+ε
...
−ε
+ε
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
+
⎡
⎢⎢⎢⎢⎢⎢⎢⎣
vd1
vd2
...
vdM −1
vdM
⎤
⎥⎥⎥⎥⎥⎥⎥⎦
(9)
where ε = A − B is the alternate wave, and vdi = vi − vi+1 .Let mi
s be the ith row in Ms ; then the TM estimates the TWAamplitude as Valt = 1
2 max(|modds − meven
s |), where modds =
Eiodd(mis) and meven
s = Eieven(mis) are the TWA templates
for odd and even alternans, respectively, and E is the expectedvalue, estimated as the sample average.
The Matrix Ms can also be columnwise analyzed in termsof time series sj , with 1 ≤ j ≤ N . The SM [1], [10] ana-lyzes TWA by means of the periodogram of each sj , given bypj = 1
M | FFT(sj )|2 , and the averaged power spectrum is ob-tained as p = Ej (pj ). Detection is made by means of the TWARatio (TWAR), given by TWAR = p0 . 5 −μn o i s e
σn o i s e, where p0.5 is
the magnitude of p at 0.5 cpb (cycles per beat) frequency bin ofthe spectrum, and μnoise (σnoise) is the mean (standard devia-tion) of the spectral noise measured in a reference spectral win-dow. In this study, this window was set to 0.33–0.48 cpb, otherworks have used a narrower spectral window starting above0.4 cpb [25], [26]. TWA is considered significant if TWAR > 3,and TWA amplitude is estimated as Valt =
√p0.5 − μnoise .
III. HYPOTHESIS TESTS AND DECISION STATISTICS
In this section, the Bootstrap resampling technique is de-scribed for its use in two different scenarios: first, for perfor-mance analysis of TWA analysis systems on a semisyntheticdataset with known TWA activity; and second, to measure theintergroup separation between two real populations for TWAamplitude estimation.
In our proposal, a set of successive comparisons is made forblock validation and optimization in a TWA analysis system.The label Model represents a whole set of processing stagesused in a TWA analysis system, with a concrete selection of thefree parameters. We define two models, so-called Model 1 andModel 2, with one single processing difference between them.We need to decide whether the performance differences betweenModel 1 and Model 2 are statistically significant in terms of agiven performance statistic. Our statistical hypothesis test willcontrast the null hypothesis (H0) that Model 1 and Model 2 havethe same performance, against the alternative hypothesis (H1)that they have different performance. Let uM 1 and uM 2 denotethe performance statistic obtained for each model, for example,the mean of TWA amplitude estimation absolute errors. Then,the hypothesis test can be stated as H0 : Δu = 0 versus H1 :Δu �= 0, with Δu = uM 2 − uM 1 .
In order to approximate the probability density function (pdf)of uM 1 , uM 2 , and subsequently of Δu, we use the well-knownplug-in principle. In brief, let Z = {zj , j = 1, . . . , L} be a setof L TWA amplitude estimation absolute errors, and let u be astatistical magnitude estimated by using an operator O on the
GOYA-ESTEBAN et al.: NONPARAMETRIC SIGNAL PROCESSING VALIDATION IN T-WAVE ALTERNANS DETECTION AND ESTIMATION 1331
Fig. 2. Histograms for the possible results of the hypothesis test: (a) Semisyn-thetic signals and (b) Holter databases.
observed set, i.e., u = O(Z). Since actual fZ (Z) is unknown,only a finite number of samples are available, and operator O canbe complex, then fu (u) will be often impractical to compute.Alternatively, we can approximate fZ (Z) for its plug-in empir-ical distribution. We build sets Z∗(b) (so-called resamples fromZ), by sampling with replacement up to L elements of Z. Now,a replication of statistic u is obtained as u∗(b) = O(Z∗(b)), andit represents an estimate of this statistic. By repeating the re-sampling procedure for b = 1, . . . , B, an estimated pdf is givenby fu (u) = 1
B
∑Bb=1 δ(u − u∗(b)). An estimation of the con-
fidence interval for Δu, can be readily obtained from orderedstatistics in Δu∗(b) resamples [27]. Bootstrap tests were per-formed with B = 500. The test determines that the differencesbetween the two models are statistically relevant in terms ofstatistic u when at least 97.5% of the B values are at one sideof the zero value.
Using both, central tendency and dispersion parameters, givesa global statistical knowledge of the data being analyzed. Inthis study, operator O stands for the mean (M ), the median(Md), the standard deviation (SD), the confidence interval width(CIW), and the power (P ), defined as P = E[Z2 ] = (E[Z])2 +Var(Z).
Regarding the analysis of the semisynthetic signal set withknown TWA activity, and for TWA estimation, Z stands forthe TWA amplitude estimation absolute errors (Ae), givenby, Aej = |aj − aj |, where aj and aj are the actual and theestimated TWA amplitudes, respectively. Therefore, uM 1 =O(Ae1
j ) and uM 2 = O(Ae2j ), where Ae1
j and Ae2j are the Aej
for Model 1 and for Model 2, respectively. Fig. 2(a) showsthe three possible results of the hypothesis test for Δu esti-mated from Δu∗(b) resamples: H0 is accepted, none of theModels is better in terms of u, since the zero value is over-lapped and less than 97.5% of the B values are at one side(top); H0 is rejected because Model 1 outperforms Model 2in terms of u, all Δu∗(b) values are positive meaning that forevery resample uM 2 is larger than uM 1 (medium); and H0is rejected because Model 2 outperforms Model 1 in terms ofu statistic since all Δu∗(b) values are negative (bottom). ForTWA detection, Z stands for the probability error (Pe), ob-tained as Pej = (FNj + FPj )/Lj , where Lj is the number ofsemisynthetic signals used to obtain each Pej and FNj , FPj
stand for false negatives and false positives, respectively. Sim-
ilarly, uM 1 = O(Pe1j ) and uM 2 = O(Pe2
j ), where Pe1j and Pe2
j
are the Pej for Model 1 and for Model 2, respectively.To measure the intergroup separation between two real popu-
lations, Z stands for the TWA amplitude estimations aj ; there-fore, uP m
M n = O((aj )P mM n ), where (aj )P m
M n are the aj for popula-tion m and Model n. In this case, we first study if Model 1 pro-vides significantly higher TWA amplitude estimations for onepopulation (P1) than for the other (P2) or viceversa, δuM 1 =uP 2
M 1 − uP 1M 1 , and the same for Model 2, δuM 2 = uP 2
M 2 − uP 1M 2 .
Furthermore, to test whether the intergroup separation betweenthe two populations is significantly higher with Model 1 orwith Model 2, the difference between the estimated distributionsδuM 1 and δuM 2 is obtained as Δu = δuM 2 − δuM 1 . Fig. 2(b)shows an example of the δu∗
M 1(b) (top), δu∗M 2(b) (medium),
and Δu∗(b) (bottom) resamples. In this example, the confi-dence intervals for δuM 1 and δuM 2 indicate that both Model 1and Model 2 provide significantly higher TWA amplitude es-timations for P2 than for P1, since all δu∗
M 1(b) and δu∗M 2(b)
values are positive. The estimated confidence interval for Δuindicates that the intergroup statistical separation between thetwo populations is significantly higher with Model 1, in termsof statistic u, since all Δu∗(b) values are negative.
Other nonparametric resampling test [28]–[30], and paramet-ric statistical algorithms [31] have been previously used in TWAstudies.
IV. EXPERIMENTS WITH SEMISYNTHETIC SIGNALS
A. Semisynthetic Signals Database
A usual methodological problem when evaluating the perfor-mance of a TWA processing system is that the actual presenceof alternans is unknown in real signals. Hence, our first experi-mental step was to generate a set of ECG signals with artificialalternant waves, in order to have a perfect knowledge of theiractual magnitude and presence.
To obtain signals as realistic as possible, 3-min records weregenerated by adding noise and alternans to a set of 5 control ECGsignals from the MIT-BIH Arrhythmia Database (fs = 360 Hz;records 103, 112, 117, 121 and 123; first lead of each record)[32]. These ECG signals were selected because 99% of theirbeats were annotated as normal, and they were found with nopositive TWA presence in [10].
An alternant wave with 35-μV amplitude was added to everyother beat. Each realization had a random probability of alter-nans inclusion, i.e., some of the resulting semisynthetic signalshad alternans, and the others did not. The alternant waves wereestimated from an ECG with clear TWA recorded during a per-cutaneous coronary intervention, from the dataset used in [16].These waves were smoothed and resampled to fit the controlECGs with fs = 360 Hz. Fig. 3 shows a heartbeat from record103, before and after alternant wave inclusion. Physiologicalnoise from the MIT-BIH Noise Stress Test Database [32] wasadded from three noise sources, namely, muscular activity arti-facts, electrode motion artifacts, and baseline wandering, for lowand high levels (15 and 25 dB) of signal-to-noise ratio (SNR).In each realization, the noise segment was extracted beginning
1332 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 4, APRIL 2014
Fig. 3. Representation of an original heartbeat from record 103 (dashed) andthe same heartbeat after the alternant wave inclusion (straight).
at a random position in the complete record and added to thecorresponding control ECG.
For TWA amplitude estimation, a set of L = 500 semisyn-thetic signals were obtained. For TWA detection, L = 50 setsof Lj = 100 signals were used to obtain 50 Pe values.
B. Model Comparisons on Semisynthetic Signals
A set of successive comparisons for block validation andoptimization was conducted on the semisynthetic signal set.
In the Preprocessing Stage, the performance of the systemwas tested in terms of CLPF, for inclusion/exclusion, BLC forinclusion/exclusion, as well as for θ1
BLC = [mean filter, medianfilter], and for θ2
BLC = [600, 700, 800, 900, 1000] ms.In the R-peak Detection Stage, the performance of the system
was tested in terms of the BPF, for θ1BPF = [10, 15, 20] Hz (and
fixing θ2BPF= 10 Hz).
In the repolarization interval segmentation and synchroniza-tion stage, we first analyzed the FLPF for its relative position inthe system, either before repolarization interval segmentation, orrow-wise in the matrix M; then, for its inclusion/exclusion; andfinally, for θ1
FLPF = [12, 15, 17, 20, 22, 25] Hz. The segmenta-tion block was tested in terms of option A and option B forθ1
T . The windowing block was tested for inclusion/exclusion.Finally, the synchronization block was analyzed for inclu-sion/exclusion, and in terms of option A and option B for θ1
SYN .
C. Results on Semisynthetic Signals
Results are summarized for TWA amplitude estimation withTM (Table I) and with SM (Table II), as well as for TWA de-tection with SM (see Table III). Each table contains, first, thevalues of each decision statistic for each SNR, for the Initialconfiguration of the TWA system, and for the Final config-uration after the system optimization procedure. The Initialconfiguration consisted of the following blocks and free param-eters: CLPF, BLC (θ1
BLC = median filter and θ2BLC = 700 ms),
BPF (θ1BPF = 7.5 Hz, θ2
BPF = 15 Hz), FLPF (ECG filtering andθ1
FLPF = 15 Hz), repolarization interval segmentation (θ1T =
option A). The mean values of the estimated confidence inter-vals for ΔMd, ΔM , ΔCIW , ΔSD, ΔP are next presented foreach model comparison described in Section IV-B. For rejectedH0 , the mean value is shown in bold, a positive (negative) signindicating that Model 1 outperforms (underperforms) Model 2.For each row in the tables, the model comparisons setup was inCLPF, BLC-1, FLPF-2 and Windowing, Model 1, and Model2 with and without the respective block; in BLC-2, Model 1
with θ1BLC = median filter and Model 2 with θ1
BLC = meanfilter; in BLC-3, θ2
BLC values were compared in pairs from thelowest to the highest, the tables show the comparison Model 1with θ2
BLC = 700 ms and Model 2 with θ2BLC = 800 ms; in BPF,
θ1BPF values were compared in pairs from the lowest to the high-
est, tables show the comparison Model 1 with θ1BPF = 10 Hz
and Model 2 with θ1BPF = 20 Hz; in FLPF-1, in Model 1 the
FLPF block before Repolarization Interval segmentation and inModel 2 filtering row-wise in the matrix M; in FLPF-3, θ1
FLPFvalues were compared in pairs from the lowest to the highest,the tables show the comparison Model 1 with θ1
FLPF = 15 Hzand Model 2 with θ1
FLPF = 17 Hz; in segmentation and syn-chronization, several comparisons were conducted combiningall the possibilities for segmentation and synchronization de-scribed in Section IV-B, the tables show the comparison of theModels which outperformed the rest, Model 1 with θ1
T = optionA and θ1
SYN = option B, and Model 2 with θ1T = option B and
θ1SYN = option A.
For TWA amplitude estimation with TM (Table I), from theInitial configuration to the Final configuration, for both 25and 15 dB, a reduction of TWA amplitude estimation errorswas achieved in terms of M , CIW , SD and P , only Mdshowed an increase. The percentage of reduction and increaseof each statistic showed that dispersion parameters were moresensible than central tendency parameters to the optimizationprocedure.
In the Preprocessing Stage, the CLPF block inclusion im-proved the performance in terms of all statistics except for Md(25 and 15 dB) and CIW (15 dB). The inclusion of the BLCblock was controversial, since Md and M indicated improve-ment without the block, and the other statistics showed either im-provement or not significant differences with the block. Study-ing particular cases, we could notice that, in general, includingthe BLC block yielded lower TWA amplitude estimations, whichimproved the estimation when alternans were not present, butworsened when they were present. In the same block, θ1
BLC =median filter resulted clearly better compared to the mean filter,and the best values for θ2
BLC , in terms of number of significantfavorable statistics, were 800 ms (25 dB), and 700 and 800 ms(15 dB). In the R-peak Detection Stage, θ1
BPF = 10 Hz out-performed both θ1
BPF = 15 Hz and 20 Hz. In the repolarizationinterval segmentation and synchronization stage, the position ofthe FLPF block before ECG segmentation was better in termsof most of the statistics. Also, most of the statistics indicatedimprovement with the inclusion of the FLPF block, all of themfor the lowest SNR. Parameter θ1
FLPF = 15 Hz was the bestin terms of number of significant statistics. The inclusion ofthe windowing block represented an improvement on the per-formance, in terms of Md, M , and P , and only SD (25 dB)indicating the opposite. Finally, the combination θ1
T = optionB and θ1
SYN = option A was better, in terms of CIW , SD andP , only Md indicating the opposite.
For TWA amplitude estimation with SM (Table II), from theinitial configuration to the final configuration, for both 25 and15 dB, a reduction of TWA amplitude estimation errors wasachieved in terms of Md, M , and P . Conversely, dispersionstatistics CIW and SD showed an increase.
GOYA-ESTEBAN et al.: NONPARAMETRIC SIGNAL PROCESSING VALIDATION IN T-WAVE ALTERNANS DETECTION AND ESTIMATION 1333
TABLE IRESULTS ON SEMI-SYNTHETIC SIGNALS
TABLE IIRESULTS ON SEMISYNTHETIC SIGNALS
TABLE IIIRESULTS ON SEMI-SYNTHETIC SIGNALS
In the preprocessing stage, and similarly to the TM, the CLPFblock inclusion improved the performance in terms of somestatistics. The inclusion of the BLC block was controversial, aswith the TM, for the same reason. Also for SM, θ1
BLC = medianfilter resulted clearly better. Slightly different, θ2
BLC = 800 ms
(25 dB) and θ2BLC = 1000 ms (15 dB) were the best in terms
of number of significantly favorable statistics. In the R-peak de-tection stage, similarly to the TM, θ1
BPF = 10 Hz outperformedboth θ1
BPF = 15 Hz and 20 Hz. In the repolarization intervalsegmentation and synchronization stage, and different from the
1334 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 4, APRIL 2014
TM, the position of the FLPF block was significant in few cases,and among them, mostly in favor of matrix M filtering. The in-clusion of the FLPF block was mostly positive for 15 dB, butnegative for 25 dB. In each θ1
FLPF comparison, the significantstatistics were in favor of the highest value until θ1
FLPF = 20 Hz.Similarly to the TM, the inclusion of the windowing block rep-resented an improvement in terms of most statistics. Finally, thecombination θ1
T = option B and θ1SYN = option A was better
for all statistics, except for Md.For TWA detection with SM (Table III), a pronounced reduc-
tion of the Pe was achieved in terms of all statistics, from theInitial configuration to the Final configuration.
In the preprocessing stage, opposite to TWA estimation, theCLPF block inclusion yielded no significant differences at all,and the inclusion of the BLC block was mostly positive. Asin estimation, θ1
BLC = median filter resulted better than themean filter, but with less number of favorable statistics, andθ2
BLC = 700 ms and 800 ms (25 dB), together with θ2BLC =
800 ms (15 dB), were the best in terms of number of significantfavorable statistics. In the R-peak detection stage, similarly toestimation, θ1
BPF = 10 Hz outperformed the other options. Inthe repolarization interval segmentation and synchronizationstage, as in estimation, the FLPF block was significant in fewcases, but in contrast to estimation, they were in favor of filteringbefore repolarization interval segmentation. The inclusion of theFLPF block was positive in terms of M and P (25 and 15 dB)and Md (15 dB). Also different from the estimation case, foreach θ1
FLPF comparison, the significant statistics were always infavor of the lowest θ1
FLPF value. The windowing block had lessimpact in detection, but it improved the performance for 15 dBin terms of Md, M , and P . Finally, and also for detection, thecombination θ1
T = option B and θ1SYN = option A was better in
terms of all statistics, except for CIW.
D. Final Configurations
For TWA amplitude estimation with TM (Table I), the opti-mization procedure, i.e., the set of successive comparisons forblock validation and optimization, and the tradeoff between re-sults for 25 and 15 dB, led to the final configuration, which con-sists of CLPF, BLC (θ1
BLC = median filter and θ2BLC = 800 ms),
BPF (θ1BPF = 10 Hz), FLPF (ECG filtering and θ1
FLPF = 15 Hz),repolarization interval segmentation (θ1
T = option B), window-ing and synchronization (θ1
SYN = option A).For the SM, the optimization procedure along with the trade-
off between the results for 15 and 25 dB and the results forestimation and detection, yielded to the same final configura-tion as for the TM, except for the block FLPF, in which matrixM filtering was selected.
V. EXPERIMENTS WITH HOLTER DATABASES
A. Holter Databases
We used two publicly available databases. On one hand, theNormal Sinus Rhythm Database (NSRDB) [32], which consistsof 18-long-term ECG recordings (about 24 h long) of subjectsreferred to the Arrhythmia Laboratory at Boston’s Beth Israel
Deaconess Medical Center, with no significant arrhythmias (5men, 26–45 years; 13 women, 20–50 years). Recordings werestored at 128 Hz and 12-bit resolution. On the other hand, theSudden Cardiac Death Database (SCDDB) [32], which consistsof 18 patients with sinus rhythm (5 with intermittent pacing), 1continuously paced, and 4 with atrial fibrillation, all of them hadsustained ventricular tachyarrhythmia, and most had an actualcardiac arrest. Only the recordings from 13 patients (from 4 to24 hours long) with underlying sinus rhythm without pacingwere used in this study (8 men, 34–80 years; 4 women, 30–82 years; 1 unknown). The recordings were stored at 250 Hzand 12-bit resolution. In both databases, the first lead of everyrecord was used for the study.
B. Model Comparisons on Holter Databases
As the actual alternans amplitude and presence is unknownin the current scenario, several model comparisons defined interms of free parameters tuning presented in Section IV-B werehard to benchmark. Notice that in this experiment, the intergroupseparation between databases was analyzed. Hence, for some ofthe blocks, only the inclusion/exclusion was compared. Finally,we also studied with this real dataset the performance of thesystem for the Discard Non Valid Beats Stage, in terms of DNVBblock inclusion/exclusion.
C. Results on Holter Databases
The initial configuration for the experiments in this sec-tion was composed of the following blocks and free parame-ters: CLPF, BLC (θ1
BLC = median filter and θ2BLC = 800 ms),
BPF (θ1BPF = 5 Hz, θ2
BPF = 15 Hz), FLPF (ECG filteringand θ1
FLPF = 15 Hz), and repolarization interval segmenta-tion (θ1
T = option A). In every model comparison described inSection V-B, the estimated confidence intervals for δuM 1 andδuM 2 allowed always to reject H0 . Both Model 1 and Model2 provided always significantly higher TWA estimated ampli-tude for SCDDB than for the NSRDB, with the SM for all thestatistics, with the TM for all statistics except for Md, whichoppositely was always significantly lower for the SCDDB.
Table IV summarizes the results (mean values of the esti-mated confidence intervals for Δu) for the intergroup TWAamplitude differences between the two databases, with the TMand with the SM. For rejected H0 , the mean value is shownin bold, a positive sign indicating that the intergroup separa-tion is significantly higher with Model 2 than with Model 1,and a negative sign indicating the opposite. For each row, themodel comparisons setup was in DNVB, CLPF, BLC, FLPF,Windowing and Normalization, Model 1, and Model 2 with andwithout the respective block; in BPF, θ1
BPF values were com-pared in pairs from the lowest to the highest (Table IV showsthe comparison Model 1 with θ1
BPF = 10 Hz, and Model 2 withθ1
BPF = 20 Hz); in Synchronization, Model 1 with θ1T = option
A and without alignment, and Model 2 with θ1T = option B and
θ1SYN = option A; in segmentation and synchronization, Model
1 with θ1T = option A and θ1
SYN = option B, and Model 2 withθ1
T = option B and θ1SYN = option A.
GOYA-ESTEBAN et al.: NONPARAMETRIC SIGNAL PROCESSING VALIDATION IN T-WAVE ALTERNANS DETECTION AND ESTIMATION 1335
TABLE IVRESULTS ON HOLTER DATABASES
Fig. 4. TWA amplitude estimations and TWAR distributions obtained with the SM, for NSRDB and SCDDB: (a) with and without the DNVB block and (b) withand without the BLC block.
In the discard nonvalid beats stage, the intergroup separationbetween NSRDB and SCDDB was significantly higher withoutthe DNVB block in terms of all statistics. However, withoutthis block, we found that artifacts yielded to spurious amplitudeestimations, mainly in SCDDB, therefore, DNVB is a necessaryblock and it was included in the remaining experiments in thissection. Fig. 4(a) shows TWA amplitude estimations distribu-tion (SM) with and without the DNVB block, for NSRDB andSCDDB. Given that the existing noise in the databases may af-fect the detection capability of the system, Fig. 4(a) also shows,the variability results corresponding to the TWAR parameter,which conveys information regarding noise variance. It can beseen that the exclusion of the DNVB block also modifies the de-tection results, in the same way as the amplitude estimation. Forthe sake of comparison, the vertical axis for both NSRDB andSCDDB results have been equalized, though for the SCDDB,the outliers of the box-plot representation extent to 987.21 μVfor TWA amplitude estimation, and to 3152 for TWAR.
In the preprocessing sage, the CLPF block did not involvea substantial difference in the final performance of the system,and only with the TM, and in terms of P , the intergroup sep-aration between the databases was significantly higher without
the CLPF block. Fig. 5(a) shows the scatter plots for TWA am-plitude estimations with the TM. Note that values close to thediagonal represent no change when including (or not) the block,whereas values below (above) the diagonal represent higher(lower) amplitude estimates when including the block. With theTM, including the BLC block in general led to lower TWAamplitudes estimations. However, when strong baseline wan-dering was present in the recording, excluding the BLC blockresulted in misleading TWA amplitude estimations. This canbe inspected by estimating the signal to baseline noise ratio asthe power of sCLPF[n] divided by the power of the residualsignal after the BLC block, resBL[n] = sBLC [n] − sCLPF[n],resulting in 109.5 ± 119.8 (mean ± std) for the NSRDB and15.65 ± 27.38 for the SCDDB. With these values, we may seethat the SCDDB is more affected by baseline noise, and exclud-ing the BLC block has a deeper impact in this database, whichleads to higher intergroup separation in terms of all statistics ex-cept for Md. For the SM, excluding the BLC block suppressedmost low amplitude detections, and only high amplitude detec-tions remained, mainly for the SCDDB [see Fig. 4(b)], hence thiswas the reason for the increased separation between databasesin terms of Md, M , and P .
1336 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 4, APRIL 2014
Fig. 5. Scatter plots of TWA amplitude estimations with the TM, for NSRDB(left) and SCDDB (right). Amplitudes in the horizontal (vertical) axis obtainedincluding (excluding): (a) CLPF, (b) FLPF and (c) windowing blocks; (d) hor-izontal axis using normalization as alignment strategy, vertical axis withoutany alignment strategy; (e) horizontal axis using RR-adjusted segmentation +synchronization, vertical using fix segmentation + synchronization.
In the R-peak detection stage, the different θ1BPF options did
not involve a substantial difference in the performance of thesystem, and the intergroup separation was only significantlyhigher with θ1
BPF = 10 Hz in terms of M with the TM.In the T-wave segmentation and synchronization stage, we
estimated the signal to HF noise ratio as the power of SBLC [n]divided by the power of the residual signal after the FLPF
Fig. 6. TWA odd (straight line) and even (dashed) templates (modds and
mevens ) without (top) and with (bottom) Tukey windowing.
block, resHF = SBLC [n] − SFLPF[n], resulting in 3.3 ± 2.88for the NSRDB and 58.74 ± 110.6 for the SCDDB. Therefore,the NSRDB is more affected by HF noise. With the TM, ex-cluding the FLPF block led to higher estimated amplitudes, butmainly for the NSRDB [see Fig. 5(b)]. For this reason, higherinter-group separation between the databases was obtained withits inclusion. Differently, with SM, when the FLPF block was ex-cluded, some low amplitude detections disappeared, but mainlyfor the SCDDB, and the databases separation became higherin terms of P . With the TM, the intergroup separation betweendatabases was significantly higher, in terms of all statistics, whenincluding the windowing block. Fig. 5(c) shows that TWA am-plitude estimations were often higher without Tukey window-ing, mostly for the NSRDB. Fig. 6 presents an example showingthat without Tukey windowing, TWA amplitude estimation canbe distorted due to lasting R wave effect (for Fig. 6(top), Valtwas 19.28 μV, and for Fig. 6(bottom) 7.08 μV). This effect alsowas present in the SM, but to a lesser extent, due to the powerspectrum averaging. The intergroup separation was significantlyhigher when including the windowing block in terms of SD andP .
The use of no alignment strategy can, in some cases, un-derestimate TWA amplitudes due to differences in RR intervallength inside an analysis window. Including the normalizationapproach (θ1
SYN = option B) had strong impact, with both theTM and the SM [see Fig. 5(d)], leading to significantly higherseparation between databases, for all statistics except for Mdwith the TM. The variable segmentation together with the syn-chronization approach (θ1
T = option B and θ1SYN = option A)
had the same effect, but mainly with the TM and for the NSRDB[see Fig. 5(e)], resulting in a significantly higher intergroup sep-aration in terms of all statistics only with the TM.
Comparing both alignment approaches (segmentation andsynchronization), the combination θ1
T = option A and θ1SYN =
option B provided higher amplitude estimations, mainly for theSCDB, and led to significantly higher intergroup separation, forall statistics (except Md with TM).
D. Final Configuration
Considering the intergroup separation as optimization cri-terion, but also taking into account the noise characteristics ofthese particular databases, the final configuration was composed
GOYA-ESTEBAN et al.: NONPARAMETRIC SIGNAL PROCESSING VALIDATION IN T-WAVE ALTERNANS DETECTION AND ESTIMATION 1337
of the following blocks and free parameters: BLC (θ1BLC =
median filter and θ2BLC = 800 ms), BPF (θ1
BPF = 10 Hz), FLPF(ECG filtering and θ1
FLPF =15 Hz), Repolarization Interval Seg-mentation (θ1
T = option A), Windowing and Synchronization(θ1
SYN = option B).
E. Effect of the Window Size
In our study, we fixed an analysis window length (L) of 128beats with 32 beats overlapping (D), however different L valuesare employed in the literature. To evaluate the effect of L, wealso simulated L = 64 (D = 16) and L = 32 (D = 8) beats toanalyze the Holter recordings.
For both the TM and the SM, and in contrast with L = 128,for L = 64 and L = 32, we obtained either no significant dif-ferences, or significantly higher TWA estimated amplitudes forthe NSRDB than for the SCDDB in terms of most of the statis-tics. The intergroup separation between NSRDB and SCDDBwas significantly higher with L = 128 than with L = 64 andL = 32, in terms of most of the statistics.
The differences obtained in the results when decreasing thevalue of L can be due to the different noise levels in the twodatabases. On one hand, in Section V-C we estimated highernoise level for the NSRDB than for the SCDDB. On the otherhand, decreasing the value of L leads to a lower noise reductioneffect due to the averaging of less beats. Therefore, decreasingL affects more to the NSRDB than to the SCDDB, yielding ahigher increase of TWA estimated amplitudes due to noise ef-fects, and leading also to a lower inter-group separation betweenthe two databases.
VI. DISCUSION AND CONCLUSION
In this study, we studied the dependence of TWA analysis sys-tems output quality with respect to several widely used signalprocessing stages. Our aim was to optimize the final perfor-mance of the system using a set of decision statistics and anonparametric hypothesis test. For this purpose, two scenarioswere chosen. First, a set of semisynthetic signals with knownTWA activity allowed a clear gold standard for benchmarking.Second, the statistical intergroup separation was used as the op-timization criterion in two publicly available Holter databases.
Results on semisynthetic signals showed that optimal freeparameters and block inclusion/exclusion differ for the TM andfor the SM, and also for detection and for estimation with theSM. After the optimization procedure, the TWA amplitude esti-mation errors were significantly reduced in terms of most of thedecision statistics. This reduction was larger with the TM thanwith the SM, and for TWA detection with the SM, the Pe waslargely reduced in terms of all of the statistics. With respect toeach analyzed block, the CLPF improved TWA amplitude esti-mation with both the TM and the SM, but it made no differencein TWA detection. The BLC block provided unclear resultsfor estimation; however, its inclusion was mostly positive fordetection, and its tuning made important differences on the per-formance of the system. The FLPF block relative position wasalso significantly influential. Its inclusion was mainly positivefor estimation and detection (except for estimation with SM for
high SNR). Finally, appropriate tuning of T-wave segmentationand synchronization also improved the final performance of thesystem.
Results on Holter databases showed that caution has to betaken when designing a system to be used in different sets ofrecordings, since their signal characteristics may be rather dif-ferent (due to noise level and type, amount of artifacts, andothers), and this has noticeable impact on the global perfor-mance. In addition, appropriate tuning of some of the processingblocks, namely, windowing, segmentation, and synchronization,yielded to a larger statistical separation between two patient pop-ulations with different documented risk of SCD, and the resultsfrom these block configurations were mostly in agreement withthe ones on semisynthetic signals. Note that the statistical inter-group separation is often used in the trials for risk stratificationanalysis, and this has been the reason to have chosen this pa-rameter as optimization criterion in this study. In order to besure that the statistical differences pointed out by the test are notdue to artifacts or noise conditions, but rather due to actual dif-ferences on the TWA phenomena between the two populations,special caution has to be taken when evaluating the blocks thatspecifically deal with noise. In this study, the SNR for differentnoise types has been estimated in order to explain the resultsaccording to the noise content.
Our objective was to present a global system optimizationprocedure, which can be used for scrutinizing and tuning anyTWA analysis system from a digital signal processing point ofview, and to have a set of tests for measuring the impact ofdifferent signal processing blocks depending on the designer’spurpose. Our efforts were not directed to propose any improve-ment to the several blocks that form the whole TWA analysissystem. Therefore, some important aspects such as, for exam-ple, the change of the phase of TWA [26] are not fully treatedin this study due to its complexity, so its study falls beyond thescope of the present study.
The widespread research in the development of TWA signalprocessing methods has led to a wide amount of algorithms withdifferent signal processing options. However, there is no clearevidence on which is the best algorithm to be used on clinicalapplications. A straightforward clinical implication is to takeinto account that, when conducting clinical trials, given a spe-cific TWA analysis method for a specific type of application(Holter recordings, stress test recordings,. . .), a previous signalprocessing optimization, to condition the signals, may substan-tially improve the performance of the system. The methodologydeveloped in this study aims to be a useful tool for this purpose.
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